Immersion and invariance adaptive tracking control for robot manipulators with a novel modified scaling factor design

The robot manipulators' tracking control problem in the presence of inertia uncertainties is addressed in this paper, and a novel dynamic scaling–based immersion and invariance (I&I) adaptive tracking controller is utilized to stabilize the proposed system. By virtue of the reconstruction method of the parameter regression matrix, this paper provides a new perspective on how to overcome the integrability obstacle typically arising in the I&I controller design through dynamic scaling and presents a new controller design method. What is more, a novel modified scaling factor is proposed as well so that the controller can be implemented without the prior knowledge of the inertia matrix's lower bound, and only the saturation function involving the scaling factor is included in the feedback gains. Finally, the numerical simulations show the validity of the proposed controller.     

Passivity‐based parameterized adaptive disturbance attenuation controller design for switched polynomial nonlinear systems

This paper is concerned with the adaptive disturbance attenuation control problem for a class of switched polynomial nonlinear systems. At first, a parameterized controller is designed to transform the switched polynomial nonlinear systems into switched Hamiltonian systems with polynomial structure. Then, combining with the solve‐parameter algorithm described in this paper, a mixed adaptive passivity and H₂/H_∞ control method is devoted. Comparing with the existing results, the obtained adaptive disturbance attenuation controller has better performance. Finally, a numerical example is given to illustrate the effectiveness of the proposed methods.     

Improved performance MRAC of linear and non-linear systems

The problem of improved performance adaptive control (IPAC) of a class of linear and non-linear systems is considered. A method for its solution is presented, the main feature of which lies in augmenting the ‘standard’ model reference adaptive controller by a signal properly designed to compensate for the effect of plant parameter uncertainty on the output error. One of the main performance improvement characteristics of the proposed IPAC is that the zero-state output error can be made arbitrarily small under standard model reference adaptive control (MRAC) assumptions in the case of linear systems, while a similar result holds true for a class of linearizable systems as well. the structure of the proposed controller is such that several existing MRAC results, such as exponential convergence of output and parameter errors in the presence of sufficiently rich reference inputs, remain valid. the proposed controller also achieves improved performance in the presence of a class of bounded disturbances and/or unmodelled dynamics as well as in the case of an adaptation switch-off.     

基于能量整形的先进静止无功发生器(ASVG)控制器设计

建立了适合能量整形和考虑系统调节动态的简化ASVG三阶模型,首次应用能量整形IDA-PBC方法设计了先进静止无功发生器(ASVG)的闭环稳定控制器。能量整形IDA-PBC方法直接使用系统能量作为存储函数,物理意义明确,较其它非线性控制器结构简单,并避免了可能产生的不期望的高增益问题,由于设计中完整地保留了系统非线性结构,不需进行任何线性化处理,较各种线性化设计方法具有更强的鲁棒性,适应系统模型和参数不精确程度效果较好。给出的仿真算例表明所提出的ASVG控制器能够在系统发生大的扰动后,ASVG安装点电压和电容器的直流电压能尽快恢复正常,控制方案有效可行。     

Multiple‐model adaptive robust dynamic surface control with estimator resetting

A multiple‐model adaptive robust dynamic surface control with estimator resetting is investigated for a class of semi‐strict feedback nonlinear systems in this paper. The transient performance is mainly considered. The multiple models are composed of fixed models, one adaptive model, and one identification model that can be obtained when the persistent exciting condition is satisfied. The transient performance of the final tracking system can be improved significantly by designing proper switching mechanism during the parameter tuning procedure. The semi‐globally uniformly ultimately bounded stability of the closed‐loop system can be easily achieved because of the framework of adaptive robust dynamic surface control. Numerical examples are provided to demonstrate the effectiveness of the proposed multiple‐model controller. Copyright © 2014 John Wiley & Sons, Ltd.     

基于能量整形的可控制动电阻暂态稳定控制器设计--单机无穷大系统篇

应用能量整形IDA-PBC方法设计了针对电力系统大干扰的可控制动电阻(TCBR)的闭环暂态稳定控制器,能量整形IDA-PBC方法直接使用系统能量作为存储函数,物理意义明确,较其它非线性控制器结构简单,并避免了可能产生的不期望的高增益问题.由于设计中完整地保留了系统非线性结构,不需进行任何线性化处理,较各种线性化设计方法具有更强的鲁棒性,适应系统模型和参数不精确程度效果较好.建立了适合能量整形和考虑系统调节动态的简化TCBR三阶模型,首次提出了用于求解能量整形匹配PDE的待定系数法用以有效设计TCBR闭合连续暂稳控制器,并详细探讨了求解匹配PDE待定系数法的理论基础,文中给出的仿真算例表明所提出的控制器有效可行.     

Robust adaptive control of nonlinearly parameterized systems with unmodeled dynamics

Many physical systems such as biochemical processes and machines with friction are of nonlinearly parameterized systems with uncertainties. How to control such systems effectively is one of the most challenging problems. This paper presents a robust adaptive controller for a significant class of nonlinearly parameterized systems. The controller can be used in cases where there exist parameter and nonlinear uncertainties, unmodeled dynamics and unknown bounded disturbances. The design of the controller is based on the control Lyapunov function method. A dynamic signal is introduced and adaptive nonlinear damping terms are used to restrain the effects of unmodeled dynamics, nonlinear uncertainties and unknown bounded disturbances. The backstepping procedure is employed to overcome the complexity in the design. With the proposed method, the estimation of the unknown parameters of the system is not required and there is only one adaptive parameter no matter how high the order of the system is and how many unknown parameters there are. It is proved theoretically that the proposed robust adaptive control scheme guarantees the stability of nonlinearly parameterized system. Furthermore, all the states approach the equilibrium in arbitrary precision by choosing some design constants appropriately. Simulation results illustrate the effectiveness of the proposed robust adaptive controller. __________ Translated from Journal of Sichuan University (Engineering Science Edition), 2005, 37(5): 148–153 (in Chinese)     

An indirect adaptive control for fully feedback linearizable discrete-time non-linear systems

An indirect adaptive control for a discrete-time non-linear system that is fully input–output linearizable is developed. The unknown parameters of the system are identified by using a multi-output RLS algorithm. Based on the certainty equivalence principle, the estimated parameters are then utilized in the controller design. Stability of the adaptively controlled closed-loop system is shown by using the Lyapunov method. Numerical simulations are included to illustrated the performance of the proposed strategy. © 1997 John Wiley & Sons, Ltd.     

A decoupled adaptive control algorithm for global state feedback stabilization of a class of nonlinear systems

A decoupled adaptive control algorithm, namely the combined dynamic gain and adaptive homogeneous domination approach, is introduced to solve the global state feedback stabilization problem for a class of uncertain nonlinear systems. Compared with the conventional adaptive backstepping/tuning functions approach, the algorithm differs in the way of constructing the estimator and handling the nonlinear drifts, and allows the adaptive control law that is decoupled via a dynamic gain to be designed only by choosing some appropriate constants. The proposed adaptive controller guarantees that all the states of the closed‐loop system are globally bounded and the system solutions converge to zero asymptotically. Both physical and academic examples are provided to demonstrate the validness of the theory. Copyright © 2014 John Wiley & Sons, Ltd.     

MAR: A multiprocessor adaptive regulator

The present state of the multiprocessor adaptive regulator (MAR) project, a prototype controller developed at the University of Bologna, is presented. The controller is designed in a distributed environment, based on the following components: a VME bus hardware, MC68000 CPU boards and DRM, a distributed real-time operating system. The project is carried out in the framework of a research programme between DEIS and Philips Italia, I&E Division. MAR represents a significant evolution of previous experiences at DEIS in the implementation of self-tuning regulators, developed both on 8-bit and 16-bit monoprocessor configurations. The prototype software is supported by the concept of a‘software machine’(SOMA) running on a‘hardware machine’(HAMA) typical of the DRM system. Particular attention is given to the definition of a user-friendly interface and to the development of supervisory features in order to obtain well-conditioned and robust performances. These features mainly deal with controller start-up, parameter estimator wind-up and actuator wind-up. Two adaptive control policies are presently available, i.e. pole-zero placement and minimum variance control. Experiments snowing the implemented functions and results obtained from different SOMA distributions are presented and discussed.     

Decentralized robust adaptive-output feedback controller for power system load frequency control

In this paper, a new model reference-decentralized robust adaptive-output feedback controller is proposed for the load frequency control (LFC) of large-scale power systems with unknown parameters. This control strategy requires only local input–output data and can follow random changes in the operating conditions. The controller is designed such that the trajectory errors and the control gains of each area remain uniformly bounded. In the proposed method, firstly an adaptive observer is designed to estimate the state variables and system parameters using local data only. Then a locally linear combination of the estimated states and the model reference states are used to design a robust adaptive-output feedback controller for each area. Simulation results for a three-area power system show that the proposed controller achieves good performance even in the presence of plant parameter changes and system non-linearities. Received: 18 October 2001/Accepted: 24 October 2001     

A globally convergent direct adaptive pole‐placement controller for nonminimum phase systems with relaxed excitation assumptions

In this paper, we propose the first solution to the long‐standing problem of designing a globally convergent direct adaptive pole‐placement controller for linear, time‐invariant discrete‐time systems with arbitrary zeros that does not rely on persistency of excitation assumptions. As is well known, the main difficulty of this design is that it involves the estimation of parameters that enter nonlinearly in the regression model. This problem can be overcome introducing an overparameterized representation of the system, which imposes very strict persistency of excitation conditions to prove the parameter convergence. The latter is avoided here using a new version of the dynamic regressor extension and mixing parameter estimator recently proposed in the literature. The main feature of this estimator is that it generates, out of an m‐dimensional vector regression, m scalar regression models. This property allows us to estimate only the controller parameters of interest for the adaptive implementation, whose convergence is ensured under assumptions that are strictly weaker than the classical persistency of excitation requirement. Simulation results that illustrate the performance of the proposed scheme are also presented.     

Output feedback tracking control for rigid body attitude via immersion and invariance angular velocity observers

A novel immersion and invariance (I&I) angular velocity observer is presented for the attitude tracking control of a rigid body with the lack of angular rate. Global exponential convergence of angular velocity estimate errors are guaranteed by an innovative filter design for the estimates' Euclidean norm. The proposed method requires fewer filter states compared with existing I&I angular velocity observer designs, which achieves a simpler closed-loop structure (dynamic reduction). The observer synthesis and convergence are independent of the control torque, which leads to much convenience in establishing “separation property” when combining a proportional-derivative attitude tracking controller driven by angular velocity estimates. A rigorous stability analysis is provided to ensure the (almost) global asymptotic convergence of the overall closed-loop tracking errors, and several numerical simulations are carried out to demonstrate the effectiveness of the combined implementation of proposed angular velocity observer and full-state feedback attitude tracking controller.     

A globally convergent wind speed estimator for wind turbine systems

An estimator of the wind speed of a wind turbine coupled to a generator is proposed in this paper. Wind speed enters into the generator dynamics through a highly nonlinear function; hence, we are confronted with a difficult problem of estimation of a nonlinearly parameterized system. To solve this problem, we use the technique of immersion and invariance, recently introduced in the literature. It is assumed that the rotor speed and electrical torque of the generator are measured, which is the case for the machines typically used in this application. The result is of interest for the design of controllers of maximum power extraction, where the knowledge of the wind speed is necessary to express the control objective as a speed tracking problem. Detailed computer simulations are presented to assess the performance of the proposed estimator.Copyright © 2012 John Wiley & Sons, Ltd.     

Mapping filtered forwarding‐based robust adaptive control for uncertain nonlinear systems with input constraint

This work develops a robust adaptive control algorithm for uncertain nonlinear systems with parametric uncertainties and external disturbances satisfying an extended matching condition. This control method is implemented in the framework of a mapping filtered forwarding‐based technique. As an attractive alternative of the adaptive backstepping method, this bottom‐up strategy forms a virtual controller and a parameter updated law at each step of the design, where Lyapunov functions and the prior knowledge of system parameters are not required. The boundedness of all signals is guaranteed by using Barbalat's lemma. According to immersion relationship, a compliant behavior of systems behaves accordingly to the lower‐order target dynamics. Furthermore, input constraints are handled by estimating a saturated scaling. A spring, mass, and damper system is used to demonstrate the controller performances via simulation results.     

Tracking control of vertical taking-off and landing vehicles with parametric uncertainty

This paper considers the position and attitude tracking control of a quadrotor with inertia parameter uncertainty. With the aid of the cascade structure of the dynamics of the system, an immersion and invariance observer is proposed to estimate the unknown mass of the system first. Secondly, a saturation controller is designed for the thrust force. Thirdly, a virtual controller is proposed for the angular velocity of the quadrotor with the aid of a nonlinear transform of the Euler angles. Finally, adaptive and robust controllers are proposed for the torque input of the quadrotor to deal with the unknown inertia moment of the system. Simulation results show the effectiveness of the proposed algorithms.     

Robust adaptive tracking control of uncertain discrete time systems

In this paper, the problem of robust adaptive tracking for uncertain discrete‐time systems is considered from the slowly varying systems point of view. The class of uncertain discrete‐time systems considered is subjected to both 𝓁_∞ to 𝓁_∞ bounded unstructured uncertainty and external additive bounded disturbances. A priori knowledge of the dynamic model of the reference signal to be tracked is not completely known. For such problem, an indirect adaptive tracking controller is obtained by frozen‐time controllers that at each time optimally robustly stabilize the estimated models of the plant and minimize the worst‐case steady‐state absolute value of the tracking error of the estimated model over the model uncertainty. Based on 𝓁_∞ to 𝓁_∞ stability and performance of slowly varying system found in the literature, the proposed adaptive tracking scheme is shown to have good robust stability. Moreover, a computable upper bound on the size of the unstructured uncertainty permitted by the adaptive system and a computable tight upper bound on asymptotic robust steady‐state tracking performance are provided. Copyright © 2005 John Wiley & Sons, Ltd.     

异步机系统非参数模型自适应控制的设计实现

针对三相交流异步电机多变量、强耦合、非线性的复杂特性,设计了一种应用OMRON CQM1H可编程控制器(PLC)的非参数模型自适应异步电机控制系统,将基于紧格式线性化的单入单出非线性离散时间系统的非参数模型自适应控制方法应用在异步电机系统中,系统设计发挥了PLC擅长开关量控制的优点,实现了异步机在不同负载下的转速稳定控制和准确定位,实验结果展示了该方法的稳定性和抑止外部干扰的有效性.     

Adaptive regulation of MIMO linear systems against unknown sinusoidal exogenous inputs

This paper deals with the adaptive regulation problem in linear multi‐input multi‐output systems subject to unknown sinusoidal exogenous inputs, where the frequencies, amplitudes, and phases of the sinusoids are unknown and where the number of sinusoids is assumed to be known. The design of an adaptive regulator for the system under consideration is performed within a set of Q‐parameterized stabilizing controllers. To facilitate the design of the adaptive regulator, triangular decoupling is introduced in part of the closed‐loop system dynamics. This is achieved through the proper selection of the controller state feedback gain and the structure of the Q parameter. Regulation conditions are then presented for the case where the sinusoidal exogenous input properties are known. For the case where the sinusoidal exogenous input properties are unknown, an adaptation algorithm is proposed to tune the Q parameter in the expression of the parameterized controller. The online tuning of the Q parameter allows the controller to converge to the desired regulator. Convergence results of the adaptation algorithm are presented. A simulation example involving a retinal imaging adaptive optics system is used to illustrate the performance of the proposed adaptive system. Copyright © 2008 John Wiley & Sons, Ltd.     

An indirect model reference adaptive controller based on the multirate sampling of the plant output

The use of sampled-data multirate-output controllers for model reference adaptive control of possibly non-stably invertible linear systems with unknown parameters is investigated. Multirate-output controllers contain a multirate sampling mechanism with different sampling period at each system output. Such a control allows us to assign an arbitrary discrete-time transfer function matrix for the sampled closed-loop system and does not make assumptions on the plant other than controllability, observability and the knowledge of two sets of structural indices, namely the controllability and the observability indices. An indirect adaptive control scheme based on these sampled-data controllers is proposed which estimates the unknown plant parameters (and consequently the controller parameters) on-line from sequential data of the inputs and the outputs of the plant, which are recursively updated within the time limit imposed by a fundamental sampling period T₀. Using the proposed adaptive algorithm, the model reference adaptive control problem is reduced to the determination of a fictitious static state feedback controller owing to the merits of multirate-output controllers. Known indirect model reference adaptive control techniques usually resort to the direct computation of dynamic controllers. The controller determination reduces to the simple problem of solving a linear algebraic system of equations, whereas in known indirect model reference adaptive control techniques, matrix polynomial Diophantine equations usually need to be solved. Moreover, persistent excitation of the continuous-time plant is provided without making any special richness assumption on the reference signals.